Most of these are more middle names than they are first names. I actually don't mind if twins don't have first names that have a certain connection, but I think that it's adorable if they share somekind of connection in their middle names.

Boy/Girl:Altair and Vega (couple from Chinese mythology; the cowherd and the Weaver Girl)William [Adelin] and Matilda (the only legitimate children of Henry I of England, Matilda later became Lady of the English and the first female sovereign of England, though she was never crowned)Asa and Alexandrina (no real connection other than being two incredibly gorgeous names)Amaury and Maude (just two incredibly gorgeous names that sound well together)Helios and Selene (brother and sister from Greek mythology; the sun and the moon)Osiris and Isis (brother and sister/husband and wife from the Egyptian mythology; the god of afterlife and the goddess of motherhood)
Jojen and Meera (badass brother and sister from A Song of Ice and Fire; aka the Reeds)
Aragorn and Galadriel (LOTR characters)

There are probably several more, but now I've been pondering enough over this.

Twin names are interesting for me because I actually know several sets of twins. I have twin nieces, my boyfriend is a twin, and I have some of my closest family friends are twins. I love the idea of getting to name twins, but the thought of having them scares me a bit haha.